1. Field of the Invention
The present invention relates to a spectral analysis of mixtures. More particularly, the present invention relates to a method and apparatus of estimating a pure spectrum and a concentration of each component constituting a mixture by performing a principal component analysis and an independent component analysis of the spectrum of the mixture.
2. Description of the Related Art
A principal component regression (PCR) is generally used to estimate a concentration of a spectrum of a mixture. PCR is a multivariate analysis including two steps. The first step is a principal component analysis (PCA), in which the measured spectrum of a mixture is decomposed into a product of a factor and a score using singular value decomposition (SVD). Typically, because the factor and the score, obtained by the SVD, do not exactly match the pure spectrum and the concentration, it is difficult to estimate the pure spectra and the concentration from the spectrum of the mixture using only PCA. For this reason, to estimate the concentration, PCR requires information in addition to the spectrum of the mixture, i.e., information on the concentration of the mixture. In the second step, the additional information, i.e., the concentration of the mixture, is regressed into the score produced by the PCA to obtain a regression vector. The regression vector, obtained from a regression equation of the score and the concentration, is a contravariant vector of pure spectra of components other than a particular component to be estimated in the mixture. However, the regression vector does not exactly match the pure spectrum of the particular component. Although the regression vector obtained by PCR enables estimation of the concentration of a particular component from the spectrum of a mixture, it is still difficult to estimate the pure spectrum of the particular component.
Consequently, it is impossible to estimate the pure spectrum of each component contained in a mixture using PCR. In addition, to estimate the concentration of each component, PCR requires an additional calibration set including accurate information on the concentration of the mixture. Further, in a case where only the information on the spectrum of a mixture is given because calibration is actually impossible, the multivariate analysis cannot be employed.